Range Resolution in FMCW Radars

ABSTRACT

The disclosure provides a radar apparatus for estimating a range of an obstacle. The radar apparatus includes a local oscillator that generates a first ramp segment and a second ramp segment. The first ramp segment and the second ramp segment each includes a start frequency, a first frequency and a second frequency. The first frequency of the second ramp segment is equal to or greater than the second frequency of the first ramp segment when a slope of the first ramp segment and a slope of the second ramp segment are equal and positive. The first frequency of the second ramp segment is equal to or less than the second frequency of the first ramp segment when the slope of the first ramp segment and the slope of the second ramp segment are equal and negative.

CROSS REFERENCES TO RELATED APPLICATIONS

This application claims priority from U.S. patent application Ser. No.14/470,414 filed on Aug. 27, 2014 which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

Embodiments of the disclosure relate generally to communication antennasand more particularly to an antenna unit in radars that assists invehicle parking.

BACKGROUND

A vehicle has parking sensors to detect an obstacle behind the vehicle.The parking sensors determine a distance of the vehicle from theobstacle using ultrasonic signals when backing a vehicle. The parkingsensor operates at ultrasonic frequencies. The parking sensor outputs anultrasonic detecting signal to detect whether any obstacle is behind therear of the vehicle and receives an ultrasonic signal as reply from theobstacle. A vehicle generally requires multiple parking sensors to coverthe entire rear of the vehicle which makes it a cost intensive solution.Also, the ultrasonic parking sensors use a time division obstacledetecting method in which each sensor sends and receives ultrasonicdetect signal in a defined time slot. Thus, the process of detectingobstacles using ultrasonic sensors is time consuming which is unsafe invehicles moving with high velocity.

Ultrasonic parking sensors require the measurement and drilling of holesin the vehicle's bumper to install transducers. There are risksassociated with drilling and mounting the transducers into the bumper.The performance of the Ultrasonic sensors is sensitive to temperatureand atmospheric conditions such as snow and rain. The performance ofultrasonic sensors is severely degraded when the sensors are coveredwith snow. In addition, the range over which the ultrasonic sensorsoperates is limited.

The use of radars in automotive applications is evolving rapidly. Radarsdo not have the drawbacks discussed above in the context of ultrasonicsensors. Radar finds use in number of applications associated with avehicle such as collision warning, blind spot warning, lane changeassist, parking assist and rear collision warning. Pulse radar and FMCW(Frequency Modulation Continuous Wave) radar are predominately used insuch applications. In the pulse radar, a signal in the shape of a pulseis transmitted from the radar at fixed intervals. The transmitted pulseis scattered by the obstacle. The scattered pulse is received by theradar and the time difference between the start of transmission of thepulse and the start of reception of the scattered pulse is proportionalto a distance of the radar from the target. For better range resolution,a narrower pulse is used which requires a high sampling rate in an ADC(analog to digital converter) used in the pulse radar. In addition,sensitivity of a pulse radar is directly proportional to the power whichcomplicates the design process of the pulse radar.

In an FMCW radar, a transmit signal is frequency modulated to generate aramp segment. An obstacle scatters the ramp segment to generate areceived signal. The received signal is received by the FMCW radar. Asignal obtained by mixing the ramp segment and the received signal istermed as an IF (intermediate frequency) signal. The frequency of the IFsignal is proportional to the distance of the obstacle from the FMCWradar. The IF signal is sampled by an analog to digital converter (ADC).A sampling rate of the ADC is proportional to the maximum frequency ofthe IF signal and the maximum frequency of the IF signal is proportionalto the range of a farthest obstacle which can be detected by the FMCWradar.

The range is the distance of the obstacle from the FMCW radar. Thus,unlike in the pulse radar, the sampling rate of the ADC in the FMCWradar is independent of the range resolution. Typically in an FMCWradar, multiple identical ramp segments are transmitted in a unit calledas frame. Range resolution defines the capability of the FMCW radar toresolve closely spaced objects. The range resolution is directlyproportional to a bandwidth of the transmitted ramp segment. Also, thetransmitted ramp is required to meet the phase noise specifications thatare needed for achieving the desired performance levels. However, it isdifficult, because of hardware limitations, for a local oscillator inthe FMCW radar to generate a ramp segment with a wide bandwidth andsimultaneously meeting the phase noise specifications. Thus, it isimportant for the FMCW radar to transmit a wide bandwidth ramp segmentfor high range resolution and at the same time maintaining optimumperformance level and accuracy.

SUMMARY

This Summary is provided to comply with 37 C.F.R. § 1.73, requiring asummary of the invention briefly indicating the nature and substance ofthe invention. It is submitted with the understanding that it will notbe used to interpret or limit the scope or meaning of the claims.

An embodiment provides a radar apparatus. The radar apparatus is usedfor estimating a range of an obstacle of one or more obstacles. Theradar apparatus includes a local oscillator that generates a first rampsegment and a second ramp segment. The first ramp segment and the secondramp segment each includes a start frequency, a first frequency and asecond frequency. The first frequency of the second ramp segment isequal to or greater than the second frequency of the first ramp segmentwhen a slope of the first ramp segment and a slope of the second rampsegment are equal and positive. The first frequency of the second rampsegment is equal to or less than the second frequency of the first rampsegment when the slope of the first ramp segment and the slope of thesecond ramp segment are equal and negative.

A transmit antenna unit is coupled to the local oscillator andconfigured to transmit the first ramp segment and the second rampsegment. A range resolution of the radar apparatus using the first rampsegment and the second ramp segment together is less than the rangeresolution of the radar apparatus using the first ramp segment and thesecond ramp segment independently.

Another embodiment provides a method of estimating a range of anobstacle of one or more obstacles with a radar apparatus. A first rampsegment and a second ramp segment are transmitted. The first rampsegment and the second ramp segment, each comprising a start frequency,a first frequency and a second frequency. The first frequency of thesecond ramp segment is equal to or greater than the second frequency ofthe first ramp segment when a slope of the first ramp segment and aslope of the second ramp segment are equal and positive. The firstfrequency of the second ramp segment is equal to or less than the secondfrequency of the first ramp segment when the slope of the first rampsegment and the slope of the second ramp segment are equal and negative.

The first ramp segment and the second ramp segment are scattered by theone or more obstacles to generate the first received signal and thesecond received signal respectively. The first ramp segment and thefirst received signal are mixed to generate a first IF (intermediatefrequency) signal, and the second ramp segment and the second receivedsignal are mixed to generate a second IF signal. The first IF signal issampled to generate a first valid data and the second IF signal issampled to generate a second valid data. A data is formed from the firstvalid data and the second valid data. A range resolution obtained fromprocessing of the data is lesser than the range resolution obtained fromthe processing of the first valid data and the processing of the secondvalid data independently.

Other aspects and example embodiments are provided in the Drawings andthe Detailed Description that follows.

BRIEF DESCRIPTION OF THE VIEWS OF DRAWINGS

FIG. 1 illustrates a radar apparatus, according to an embodiment;

FIG. 2 illustrates waveforms generated by a local oscillator as afunction of time, in a radar apparatus, according to an embodiment;

FIG. 3 illustrates waveforms generated and received by a radarapparatus, according to an embodiment;

FIG. 4 illustrates waveforms generated by a local oscillator as afunction of time, in a radar apparatus, according to an embodiment; and

FIG. 5 illustrates waveforms generated by a local oscillator as afunction of time, in a radar apparatus, according to an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 illustrates a radar apparatus 100, according to an embodiment. Inone example, the radar apparatus 100 is used for estimating a range ofan obstacle of one or more obstacles. The radar apparatus 100 includes atransmit antenna unit 102 and a receive antenna unit 104. In an example,a single antenna unit functions as the transmit antenna unit 102 and thereceive antenna unit 104. A local oscillator 106 is coupled to thetransmit antenna unit 102. A receiver front-end 108 is coupled to thereceive antenna unit 104.

A mixer 110 is coupled to the local oscillator 106 and the receiverfront-end 108. An analog to digital converter (ADC) 112 is coupled tothe mixer 110. A synchronization block 114 is coupled to the localoscillator 106 and the ADC 112. A digital signal processor (DSP) 116 iscoupled to the ADC 112. The radar apparatus 100 may include one or moreadditional components known to those skilled in the relevant art and arenot discussed here for simplicity of the description.

The operation of the radar apparatus 100 illustrated in FIG. 1 isexplained now. The local oscillator 106 generates a plurality of rampsegments. The plurality of ramp segments includes a first ramp segmentand a second ramp segment. A slope of each ramp segment of the pluralityof ramp segments generated by the local oscillator 106 is same.Therefore, a slope of the first ramp segment is equal to a slope of thesecond ramp segment. In an example, the local oscillator 106 includes aPLL (phase locked loop) that generates the first ramp segment and thesecond ramp segment.

In one example, a frequency of the ramp segments generated by the localoscillator 106 is digitally controlled by a register. In anotherexample, the register controls a value of divide-by-N which is used in afeedback loop of the local oscillator 106. In a further example, thelocal oscillator 106 includes a first voltage controlled oscillator(VCO) and a second VCO that generates the first ramp segment and thesecond ramp segment respectively. In yet another example, a PLL includesthe first VCO and the second VCO generating the first ramp segment andthe second ramp segment respectively.

In an additional example, the local oscillator 106 includes a pluralityof VCO's that generates a plurality of ramp segments. A time differencebetween generation of the first ramp segment and the second ramp segmentincludes a time taken in the local oscillator 106 to switch from thefirst VCO to the second VCO. In an example, the local oscillator 106 hasa plurality of VCO's and each VCO has a predefined operating frequencyrange. The operating frequency range of each VCO of the plurality ofVCO's is either contiguous or overlapping. Only one VCO of the pluralityof VCO's is operational at a time instant.

A multiplexer is used, in one example, to select which VCO shouldoperate at a given time instant. In another example, the localoscillator 106 includes a voltage controlled oscillator (VCO). The VCOincludes a first tuning element and a second tuning element thatgenerates the first ramp segment and the second ramp segmentrespectively. The operation of the local oscillator 106 is furtherexplained later in the description with the help of FIG. 2 to FIG. 5.

The transmit antenna unit 102 transmits the first ramp segment and thesecond ramp segment. The first ramp segment and the second ramp segmentare scattered by the one or more obstacles to generate a first receivedsignal and a second received signal respectively. The receive antennaunit 104 receives the first received signal and the second receivedsignal. In one version, the first received signal includes a pluralityof delayed versions of the first ramp segment and the second receivedsignal includes a plurality of delayed versions of the second rampsegment.

In another version, when the plurality of ramp segments are transmittedby the transmit antenna unit 102, the receive antenna unit 104 receivesa plurality of received signals. The receiver front-end 108 amplifiesthe first received signal and the second received signal. The mixer 110mixes the first ramp segment and the first received signal to generate afirst IF (intermediate frequency) signal. Also, the mixer 110 mixes thesecond ramp segment and the second received signal to generate a secondIF signal.

Each ramp segment includes a start frequency, a first frequency and asecond frequency. Therefore, the first ramp segment and the second rampsegment each include the start frequency, the first frequency and thesecond frequency. In an example, the first frequency is less than thesecond frequency. Around trip delay is defined as a time differencebetween start of transmission of a ramp segment and start of receptionof the corresponding received signal from an obstacle of the one or moreobstacles. A maximum round trip delay is defined as a time differencebetween start of transmission of the first ramp segment and start ofreception of the first received signal from a farthest obstacle of theone or more obstacles.

The farthest obstacle is an extreme obstacle which can be detected bythe radar apparatus 100. The start frequency is less than the firstfrequency by at least a product of an absolute value of the slope of thefirst ramp segment and the maximum round trip delay when the slope ofthe first ramp segment and the second ramp segment are equal andpositive. The start frequency is greater than the first frequency by atleast a product of an absolute value of the slope of the first rampsegment and the maximum round trip delay when the slope of the firstramp segment and the second ramp segment are equal and negative.

In one example, the first frequency of the second ramp segment is equalto or greater than the second frequency of the first ramp segment whenthe slope of the first ramp segment and a slope of the second rampsegment are equal and positive. In another example, the first frequencyof the second ramp segment is equal to or less than the second frequencyof the first ramp segment when the slope of the first ramp segment and aslope of the second ramp segment are equal and negative.

The ADC 112 samples the first IF signal from a time instant when thefirst ramp segment is at the first frequency to a time instant when thefirst ramp segment is at the second frequency. The ADC 112 generates afirst valid data from sampling of the first IF signal. Thesynchronization block 114 provides a data valid signal to the ADC 112from the time instant when the first ramp segment is at the firstfrequency to the time instant when the first ramp segment is at thesecond frequency i.e. the synchronization block 114 provides the datavalid signal to the ADC 112 during sampling of the first IF signal.

The ADC 112 also samples the second IF signal from a time instant whenthe second ramp segment is at the first frequency to a time instant whenthe second ramp segment is at the second frequency. The ADC 112generates a second valid data from sampling of the second IF signal. Thesynchronization block 114 provides a data valid signal to the ADC 112from the time instant when the second ramp segment is at the firstfrequency to the time instant when the second ramp segment is at thesecond frequency i.e. the synchronization block 114 provides the datavalid signal to the ADC 112 during sampling of the second IF signal.

The DSP 116 further processes the first valid data and the second validdata to estimate a range of the obstacle of the one or more obstacles.The DSP 116 processes a data formed from the first valid data and thesecond valid data such that a range resolution obtained from processingof the data is less than the range resolution obtained from theprocessing of the first valid data and the processing of the secondvalid data independently. It is to be noted that the range resolution isdefined as a smallest distance between two obstacles that is resolvableby the radar apparatus 100.

For example a radar apparatus with a range resolution of 5 cm is betterthan a radar apparatus with a range resolution of 10 cm. Thus,performance of a radar apparatus with a less resolution is better. Inone example, the range resolution obtained from the processing of thedata corresponds to at least a sum of a bandwidth of the first rampsegment and a bandwidth of the second ramp segment. The range resolutionof a radar apparatus 100 is inversely proportional to the bandwidth andis defined as:

R=c/2B

where, B is the bandwidth of a signal transmitted by the radar apparatus100 and c is the speed of light. In another example, the bandwidth ofthe first ramp segment is B1 and the bandwidth of the second rampsegment is B2, the range resolution of the radar apparatus 100 isdefined as:

R=c/2(B1+B2)

In one example, B1 is equal to B2. In another example, the rangeresolution of the radar apparatus 100 is a function of the bandwidth ofthe first ramp segment and the bandwidth of the second ramp segment. Inan additional example, the range resolution of the radar apparatus 100is inversely proportional to the difference between the second frequencyof the second ramp segment and the first frequency of the first rampsegment. In an embodiment, the DSP 116 further processes a plurality ofvalid data received from the ADC 112 to estimate range of the one ormore obstacles. The operation of the DSP 116 is explained later in thedescription.

FIG. 2 illustrates waveforms generated by a local oscillator 106 as afunction of time, in a radar apparatus, according to an embodiment. Thewaveforms illustrated in FIG. 2 are illustrated in connection with theradar apparatus 100. The local oscillator 106 generates a plurality oframp segments. The plurality of ramp segments includes a first rampsegment 202 and a second ramp segment 204. A slope of the first rampsegment 202 is equal to a slope of the second ramp segment 204. In oneexample, the slope of the first ramp segment 202 is not equal to theslope of the second ramp segment 204. In another example, the localoscillator 106 is a PLL (phase locked loop) that generates the firstramp segment 202 and the second ramp segment 204.

In yet another example, a PLL includes the first VCO and the second VCOgenerating the first ramp segment 202 and the second ramp segment 204respectively. The first ramp segment 202 has a start frequency fc0 208,a first frequency fc1 210 and a second frequency fc2 212. The secondramp segment 204 has a start frequency fc4 214, a first frequency fc2212 and a second frequency fc3 216. It is to be noted that the secondfrequency fc2 212 of the first ramp segment 202 is equal to the firstfrequency fc2 212 of the second ramp segment 204.

In one example, the first frequency fc2 212 of the second ramp segment204 is equal or greater than the second frequency fc2 212 of the firstramp segment 202. In another example, the local oscillator 106 includesa first voltage controlled oscillator (VCO) and a second VCO thatgenerates the first ramp segment 202 and the second ramp segment 204respectively. In an additional example, the local oscillator 106includes a plurality of VCO's that generates a plurality of rampsegments. In yet another example, the local oscillator 106 includes avoltage controlled oscillator (VCO). The VCO includes a first tuningelement and a second tuning element that generates the first rampsegment 202 and the second ramp segment 204 respectively.

In an example, a round trip delay is defined as a time differencebetween start of transmission of a ramp segment and start of receptionof the corresponding received signal from an obstacle of the one or moreobstacles. A maximum round trip delay is defined as a time differencebetween start of transmission of the first ramp segment 202 and start ofreception of the first received signal from a farthest obstacle of theone or more obstacles. The farthest obstacle is an extreme obstaclewhich can be detected by the radar apparatus 100.

The start frequency is less than the first frequency by at least aproduct an absolute value of the slope of the first ramp segment 202 andthe maximum round trip delay when the slope of the first ramp segment202 and the second ramp segment 204 are equal and positive. The startfrequency is greater than the first frequency by at least a product ofan absolute value of the slope of the first ramp segment 202 and themaximum round trip delay when the slope of the first ramp segment 202and the second ramp segment 204 are equal and negative. The time Tc1 220defines a duration of the first ramp segment 202 and the time Tc2 222defines a duration of the second ramp segment 204. In one example, Tc1220 is equal to Tc2 222.

The time Tgap 224 includes a time taken in the local oscillator 106 toswitch from the first VCO to the second VCO or to switch from the firsttuning element to the second tuning element. In one example, the timeTgap 224 includes a time required for the local oscillator 106 to settleafter switching from the first VCO to the second VCO or from the firsttuning element to the second tuning element. The time Tgap 224 alsorepresents a time difference between generation of the first rampsegment 202 and the second ramp segment 204.

A time difference between start of transmission of the second rampsegment 204 and start of reception of the second received signal fromthe farthest obstacle of the one or more obstacles is represented as τ2240 and equals the difference of t3 and t3′. From the time instant t3′,the second VCO is assumed to be generating a steady second ramp segment204. Similarly, τ1 238 is a time difference between start oftransmission of the first ramp segment 202 and start of reception of thefirst received signal from the farthest obstacle of the one or moreobstacles.

The ADC 112 samples the first IF signal from a time instant t1 230 to atime instant t2 232 and generates a first valid data. The ADC 112samples the second IF signal from a time instant t3 234 to a timeinstant t4 236 to generate a second valid data. The synchronizationblock 114 provides a data valid signal to the ADC 112 during thesampling of the first IF signal and during the sampling of the second IFsignal. Thus, the synchronization block 114 synchronizes the operationof the local oscillator 106 and the ADC 112.

The first valid data and the second valid data from the ADC 112 areprovided to the DSP 116 for further processing. In one example, thesecond frequency fc2 212 of the first ramp segment 202 is equal to thefirst frequency fc2 212 of the second ramp segment 204. Depending on thevelocity of the obstacle and the value of Tgap, there can be phasediscontinuity between the first valid data and the second valid data.This phase discontinuity needs to be corrected. This phase discontinuityis given by:

$\begin{matrix}{{\Delta\varphi} = \frac{4\pi \; f_{c\; 1}{vT}_{gap}}{c}} & (1)\end{matrix}$

where v is the velocity of the obstacle and c is the speed of light. Itis evident from the above equation (1) that the phase discontinuity isdependent on the product of the velocity of the obstacle and Tgap.Hence, the DSP 116 compares a threshold and a product of a velocityestimate of the obstacle and the time difference between a time instantwhen the first ramp segment 202 is at the second frequency and a timeinstant when the second ramp segment 204 is at the start frequency (Tgap224). This threshold is given as:

$\begin{matrix}{\left( {v_{est}T_{gap}} \right)_{thresh} = \frac{\Delta \; \varphi_{{ma}\; x}c}{4\pi \; f_{c\; 1}}} & (2)\end{matrix}$

where, v_(est) is the velocity estimate of the obstacle with respect tothe radar apparatus 100, Δϕ_(max) is a maximum phase discontinuity thatcan be tolerated between the first IF signal and the second IF signal,and c is the velocity of light.

A value of v_(est)*T_(gap) is compared to the threshold. The value ofv_(est)*T_(gap) is different for different applications. In one example,the value of Tgap is known apriori based on the design of the localoscillator 106. In another example, the maximum value of v_(est) mayalso be known apriori based on the type of application. Alternatively,v_(est) may also be dynamically estimated as described later in thisdescription. In yet another example, the maximum phase discontinuitythat can be tolerated by a specific application is ascertained and thenthe maximum value of v_(est)*T_(gap) is computed for the specificapplication and compared to the threshold; the threshold being computedas illustrated in the above equation (2).

In one example, when second frequency fc2 212 of the first ramp segment202 is equal to the first frequency fc2 212 of the second ramp segment204, the DSP 116 performs at least one of a concatenation technique, amodified concatenation technique, a modified 1D-FFT (1-dimensional fastfourier transform) technique and a modified 2D-FFT (2-dimensional fastfourier transform) technique. In another example, when second frequencyfc2 212 of the first ramp segment 202 is equal to the first frequencyfc2 212 of the second ramp segment 204, the DSP 116 compares thethreshold and the product of a velocity estimate of the obstacle and thetime difference between the time instant the first ramp segment 202 isat the second frequency and the time instant when the second rampsegment 204 is at the start frequency.

When the product of the velocity estimate of the obstacle and the timedifference (between the time instant when the first ramp segment 202 isat the second frequency and the time instant when the second rampsegment 204 is at the start frequency) is below the threshold, the DSP116 performs the concatenation technique. When the product of thevelocity estimate of the obstacle and the time difference (between thetime instant when the first ramp segment 202 is at the second frequencyand the time instant when the second ramp segment 204 is at the startfrequency) is above the threshold, the DSP 116 is configured to performsat least one of the modified concatenation technique, the modified1D-FFT technique and the modified 2D-FFT technique.

The concatenation technique, the modified concatenation technique, themodified 1D-FFT technique and the modified 2D-FFT technique are nowdescribed.

In the concatenation technique, the DSP 116 concatenates the first validdata and the second valid data to generate a concatenated data. The DSP116 further performs fast fourier transform on the concatenated data togenerate an FFT vector such that the FFT vector is processed to estimaterange of the obstacle of the one or more obstacles. In an example, aplurality of first valid data and a plurality of second valid data areobtained when a plurality of the first ramp segments and a plurality ofthe second ramp segments are transmitted by the radar apparatus 100.Each transmission of the first ramp segment is being followed by atransmission of the second ramp segment. A 2D FFT (2 dimensional fastfourier transform) is performed on the obtained valid data to estimateboth a range and relative velocity of the one or more obstacles.

Thus, for a specific application when the value of v_(est)*Tgap is belowthe threshold, the DSP 116 is oblivious to the fact that theconcatenated data was generated using multiple ramps segments and with atime difference between consecutive ramp segments. The DSP 116 processesthe data as if it were a single contiguous ramp that the spans thebandwidth from fc1 210 to fc3 216. The DSP 116 processing is independentof the value of the time Tgap 224.

In the modified concatenation technique, the DSP 116 multiplies thesecond valid data with a complex phasor to generate a modified secondvalid data. The complex phasor is exp(−jΔφ) where Δφ is the phasediscontinuity between the first IF signal and the second IF signal. Thephase discontinuity Δφ is measured using equation 1, where v is avelocity estimate of the obstacle. The DSP 116 further concatenates thefirst valid data and the modified second valid data to generate aconcatenated data and then performs fast fourier transform on theconcatenated data to generate an FFT vector such that the FFT vector isprocessed to estimate a range of the obstacle of the one or moreobstacles.

In the modified 1D-FFT technique, the DSP 116 performs fast fouriertransform on the first valid data and the second valid data to generatea first FFT vector and a second FFT vector respectively. The first FFTvector and the second FFT vector each includes a plurality of elements.The DSP 116 multiplies each element of the plurality of elements of thesecond FFT vector with a complex phasor to generate a modified secondFFT vector. A phase of the complex phasor is a function of an index ofan element of the second FFT vector and v_(est)*Tgap.

The DSP 116 adds the modified second FFT vector and the first FFT vectorto generate a single FFT vector such that the single FFT vector isprocessed to estimate a range of the obstacle of the one or moreobstacles. This procedure is illustrated now with an example. We assumethat F₁ ^(2N)(m) and F₂ ^(2N)(m) represents the first FFT vector and thesecond FFT vector respectively. N represents a number of samples in eachof the first valid data and the second valid data. The superscript (2N)represents number of elements in the first FFT vector and the second FFTvector and m represents an index of an element of the corresponding FFTvector. Thus F₁ ^(2N)(m) and F₂ ^(2N)(m) represents the m^(th) bin ofthe 2N point FFT of the N time domain samples of the first valid dataand the second valid data respectively. Thereby, the single FFT vectoris represented as:

F ^(2N)(m)=F ₁ ^(2N)(m)+e ^(−j(πm+Δϕ) ^(m) ⁾ F ₂ ^(2N)(m);0≤m≤2N−1  (3)

where Δϕ_(m) is the phase discontinuity calculated for an obstacle witha range corresponding to the index m. The value of Δϕ_(m) can becalculated using equation (1) with v being the velocity estimate of theobstacle with a range corresponding to the index m.

In the modified 2D-FFT technique, a transmit signal comprising the firstramp segment 202 and the second ramp segment 204 (shown in FIG. 2) istransmitted N_(v) times in a frame, the repetition rate of the transmitsignal being 1/T_(r). Each instance of the transmit signal results in atotal of 2N valid ADC samples (N samples corresponding to the firstvalid data and N samples corresponding to the second valid data). Afirst 2N×N_(v) point 2D FFT is performed on the N×N_(v) ADC samplescorresponding to the first valid data across the N_(v) transmissions.

The N×N_(v) ADC samples can be appropriately zero padded to create thisFFT. The first 2D FFT array is denoted by F₁ ^(2N,N) ^(v) (n, n_(v)),where the superscript (2N, N_(v)) denotes the dimensions of the FFT and(n, n_(v)) are the index into the 2D FFT bins. Note that n ranges from 0to 2N−1 and n_(v) ranges from 0 to N_(v)−1. Similarly a second 2N×N_(v)point 2D FFT is performed on the N×N_(v) ADC samples corresponding tothe second valid data across the N_(v) transmissions. The N×N_(v) ADCsamples can be appropriately zero padded to create this FFT. The second2D FFT array being denoted by F₂ ^(2N,N) ^(v) (n, n_(v)).

The first 2D FFT array and the second 2D FFT array each includes aplurality of elements arranged in a 2D matrix indexed by two indices (n,n_(v)). Each element of the plurality of elements of the second 2D FFTarray is multiplied with a complex phasor to generate a modified second2D FFT array. The first 2D FFT array and the modified second 2D FFTarray are then coherently added to generate a single 2D FFT array givenas follows:

$\begin{matrix}{{{F^{{2N},N_{v}}\left( {n,n_{v}} \right)} = {F_{1}^{{2N},N_{v}} + {{\alpha \left( {n,n_{v}} \right)}{F_{2}^{{2N},N_{v}}\left( {n,n_{v}} \right)}}}}{{{where}\mspace{14mu} {\alpha \left( {n,n_{v}} \right)}} = e^{- {({{j\; \pi \; n} + \frac{2\pi \; n_{v}T_{gap}}{T_{r}N_{v}}})}}}} & (4)\end{matrix}$

Thus in equation 4, each element in the second 2D FFT is multiplied bythe complex phasor and is then added to the corresponding element in thefirst 2D FFT array to create a single 2D FFT array. A phase of thecomplex phasor is a function of the two indices and the time differencebetween the time instant when the first ramp segment 202 is at thesecond frequency and the time instant when the second ramp segment 204is at the start frequency. This single 2D FFT array can then beprocessed to estimate the range and velocity of an obstacle of one ormore obstacles. This technique does not require prior computation of thevelocity estimate v_(est), instead the velocity estimation is seamlesslyincorporated into the 2D FFT process.

In another example, when the second frequency of the first ramp segment202 is not equal to the first frequency of the second ramp segment 204,the DSP 116 concatenates the first valid data, a plurality of paddingsamples and the second valid data to generate a concatenated data. TheDSP 116 performs fast fourier transform on the concatenated data togenerate an FFT vector such that the FFT vector is processed to estimatea range of the obstacle

It is to be noted that some of the described techniques require thevelocity estimate ‘v_(est)’ of the obstacles. The velocity estimate‘v_(est)’ of the obstacle with respect to the radar apparatus 100 isobtained using the following procedure. The local oscillator 106generates a plurality of the first ramp segments. The transmit antennaunit 102 transmits the plurality of first ramp segments as a part of aframe. The plurality of the first ramp segments are scattered by the oneor more obstacles to generate a plurality of a first received signals.

The receive antenna unit 104 receives a plurality of the first receivedsignals. The receiver front-end 108 amplifies the plurality of the firstreceived signals. The mixer 110 mixes the plurality of the first rampsegments and the plurality of the first received signals to generate aplurality of IF signals. The ADC 112 samples the plurality of IFsignals. The DSP 116 performs 2D fast fourier transform (FFT) on theplurality of IF signals to obtain a coarse estimated of a range and acorresponding velocity estimate of the obstacle of the one or moreobstacles. In an embodiment, the velocity estimate ‘v_(est)’ is obtainedby any of the techniques known in the art. It is to be noted, that thedescribed method for velocity estimation uses the first ramp segment.However, other embodiments may use the second ramp segment instead. Yetother embodiments can use any ramp segment which is contiguouslygenerated by the local oscillator 106.

In the concatenation technique the DSP 116 is oblivious to the fact thatthe concatenated data was generated using multiple VCO's that generatesmultiple ramps segments with a time difference between consecutive rampsegments. The DSP 116 processes the concatenated data as if the transmitsignal was a single ramp from frequency fc1 210 to frequency fc2 216.Further, the modified concatenation, the modified 1D-FFT and themodified 2D-FFT techniques while not completely transparent, requireonly minimal changes in the DSP 116 as explained earlier.

It is understood that the above procedures are explained using anembodiment with the first ramp segment 202 and the second ramp segment204 and it can be extended to a plurality of ramp segments by repeatingthe same procedures. Thus, the bandwidth of a transmitted signal fromthe radar apparatus 100 is increased by transmitting a plurality of rampsegments and thereby improving the range resolution of the radarapparatus 100 without being limited by the range of a single VCO or of atuning element.

Further the embodiments used to generate the concatenated data aretransparent to a signal processing software that resides on the DSP 116and performs the radar signal processing. Hence, the signal processingsoftware residing on the DSP 116 will require little or no customizationin order to process ADC samples obtained using the above describedembodiments. An important feature of the embodiment is that there is noneed to maintain a phase continuity across the first ramp segment 202generated from the first VCO and the second ramp segment 204 generatedfrom the second VCO. This is explained in detail in the followingparagraphs.

FIG. 3 illustrates waveforms generated and received by a radarapparatus, according to an embodiment. The waveforms illustrated in FIG.3 are illustrated in connection with the radar apparatus 100. A rampsegment 345 is transmitted by the radar apparatus 100 and a receivedsignal 350 is received by the radar apparatus 100. The ramp segment 345is scattered by one or more obstacles. The received signal 350 isgenerated by an obstacle of the one or more obstacles. The receivedsignal 350, illustrated in FIG. 3, is also a ramp segment and representsa delayed version of the ramp segment 345. The ramp segment 345 has aslope S Hz/s, an initial frequency fc and an initial phase ϕ₀. The phaseof the ramp segment 345 is defined as:

$\begin{matrix}{{\varphi_{TX}(t)} = {{2{\pi\left( {{f_{c}t} + \frac{{St}^{2}}{2}} \right)}} + \varphi_{o}}} & (5)\end{matrix}$

Around trip delay (τ) 352 is defined as a time difference between startof transmission of the ramp segment 345 and start of reception of thereceived signal 350 from the one or more obstacles. τ_(max) 354 is themaximum round trip delay and represents a time difference between startof transmission of the ramp segment 345 and start of reception of thereceived signal 350 from a farthest obstacle of the one or moreobstacles. The farthest obstacle is an extreme obstacle which can bedetected by the radar apparatus 100. The phase of the received signal350 with the round trip delay of T seconds is defined as:

$\begin{matrix}{{\varphi_{RX}(t)} = {{\varphi_{TX}\left( {1 - \tau} \right)} = {{2{\pi\left( {{f_{c}\left( {t - \tau} \right)} + \frac{{S\left( {t - \tau} \right)}^{2}}{2}} \right)}} + \varphi_{o}}}} & (6)\end{matrix}$

The mixer 110 mixes the ramp segment 345 and the received signal 350 togenerate an IF (intermediate frequency) signal. The phase of the IFsignal is defined as:

$\begin{matrix}\begin{matrix}{{\varphi_{IF}(t)} = {{\varphi_{TX}(t)} - {\varphi_{TX}\left( {t - \tau} \right)}}} \\{{= {{2\pi \left( {{f_{c}t} - \frac{S\; \tau^{2}}{2}} \right)} + {2{\pi S}\; \tau \; t}}};\left( {\tau_{{ma}\; x} < t < T_{c}} \right)}\end{matrix} & (7)\end{matrix}$

A time Tc 356 defines the length or duration of the ramp segment 345.Now, equation 7 is used to evaluate the first ramp segment 202 and thesecond ramp segment 204 illustrated in FIG. 2. The phase of the IFsignal corresponding to the first ramp segment 202 is defined as:

$\begin{matrix}\begin{matrix}{{\varphi_{{IF}\; 1}(t)} = {\varphi \left( {t - \tau} \right)}} \\{= {{2{\pi\left( {{f_{c\; 0}\tau} - \frac{S\; \tau^{2}}{2}} \right)}} + {2\pi \; S\; \tau \; {t\left( {\tau_{{ma}\; x} < t < T_{c}} \right)}}}}\end{matrix} & (8)\end{matrix}$

Where fc0 208 is the start frequency of the first ramp segment 202. Thephase of the IF signal corresponding to the second ramp segment 204 interms of a variable t′ is defined as:

$\begin{matrix}{{\varphi_{{IF}\; 2}\left( t^{\prime} \right)} = {{2{\pi\left( {{f_{c\; 4}\tau} - \frac{S\; \tau^{2}}{2}} \right)}} + {2\pi \; S\; \tau \; t^{\prime}\mspace{14mu} \left( {\tau_{{m\; {ax}}\;} < t^{\prime} < T_{c}} \right)}}} & (9)\end{matrix}$

Where fc4 is the start frequency of the second ramp segment 204. Tc1 220is equal to Tc2 222 and represented as Tc. Since the second ramp segment204 follows the first ramp segment 202, t′ is defined as:

t=t′+T _(c) +T _(gap);  (10)

i.e; t′=t−T _(c) −T _(gap)  (11)

Replacing t′ in equation 9:

$\begin{matrix}{{{{\varphi_{{IF}\; 2}(t)} = {{2{\pi\left( {{f_{c\; 4}\tau} - \frac{S\; \tau^{2}}{2}} \right)}} + {2\pi \; S\; {\tau \left( {t - T_{c} - T_{gap}} \right)}}}};}\left\{ {{\tau_{m\; {ax}} + T_{c} + T_{gap}} < t < {{2T_{c}} + T_{gap}}} \right\}} & (12)\end{matrix}$

The start frequency fc4 of the second ramp segment 204 is defined as:

f _(c4) =f _(c0) +ST _(c) −Sτ _(max)  (13)

Replacing fc4 in equation 12:

$\begin{matrix}{{{{\varphi_{{IF}\; 2}(t)} = {{2{\pi\left( {{f_{c\; 0}\tau} - \frac{S\; \tau^{2}}{2} - {S\; {\tau\tau}_{m\; {ax}}}} \right)}} + {2\pi \; S\; {\tau \left( {t - T_{gap}} \right)}}}};}\left\{ {{\tau_{{ma}\; x} + T_{c} + T_{gap}} < t < {{2T_{c}} + T_{gap}}} \right\}} & (14)\end{matrix}$

Equation 14 is further simplified and the following equation isobtained:

$\begin{matrix}{{{{\varphi_{{IF}\; 2}(t)} = {{2{\pi\left( {{f_{c\; 0}\tau} - \frac{S\; \tau^{2}}{2} - {S\; {\tau \left( {\tau_{m\; {ax}} + T_{gap}} \right)}}} \right)}} + {2\pi \; S\; \tau \; t}}};}\left\{ {{\tau_{m\; {ax}} + T_{c} + T_{gap}} < t^{\prime} < {{2T_{c}} + T_{gap}}} \right\}} & (15)\end{matrix}$

Comparing equation 8 and equation 15, we note that the frequency term(2πSτt) in the IF signal corresponding to the first ramp segment 202 isequal to the frequency term (2πSτt) in the IF signal corresponding tothe second ramp segment 204. In addition, it is noted that the phase ofthe IF signal corresponding to the first ramp segment 202 at t=Tc isequal to the phase of the IF signal corresponding to the second rampsegment 204 at t=τ_(max)+T_(c)+T_(gap). Hence, both phase and frequencycontinuity is maintained from the first ramp segment 202 to the secondramp segment 204 and therefore both the IF signals (IF1 and IF2) can beseamlessly combined together. The above illustration assumes that theone or more obstacles are stationary with respect to the radar apparatus100. In case an obstacle has a velocity v, then the phase discontinuitybetween the two IF signals is given by equation 1.

FIG. 4 illustrates waveforms generated by a local oscillator 106 as afunction of time, in a radar apparatus, according to an embodiment. Thewaveforms illustrated in FIG. 4 are illustrated in connection with radarapparatus 100. The local oscillator 106 generates a plurality of rampsegments. The plurality of ramp segments includes a first ramp segment480 and a second ramp segment 482.

The first ramp segment 480 and the second ramp segment 482 are generatedat a same time instant t1′. In an example, the start of the second rampsegment 482 is before an end of the first ramp segment 480. A slope ofthe first ramp segment 480 is equal to a slope of the second rampsegment 482. In one example, the slope of the first ramp segment 480 isnot equal to the slope of the second ramp segment 482.

In one version, the local oscillator 106 has a pair of PLL's (phaselocked loop) that generates the first ramp segment 480 and the secondramp segment 482 simultaneously. In another version, the localoscillator 106 includes a first voltage controlled oscillator (VCO) anda second VCO that generates the first ramp segment 480 and the secondramp segment 482 simultaneously. In yet another version, the radarapparatus 100 includes two chips each having a VCO (or PLL) thatgenerates the first ramp segment 480 and the second ramp segment 482simultaneously.

Also, the radar apparatus 100 would include two ADCs and two mixers toprocess the received ramp signals simultaneously. The second rampsegment 482 has a start frequency fc3 485, a first frequency fc2 486 anda second frequency fc3 487. Similarly, the first ramp segment 480 has astart frequency fc0 488, a first frequency fc1 489 and a secondfrequency fc2 486. It is to be noted that the second frequency of thefirst ramp segment 480 is equal to the first frequency of the secondramp segment 482. In an example, the second frequency of the first rampsegment 480 is not equal to the first frequency of the second rampsegment 482.

The embodiment of FIG. 4 spans the same bandwidth as the embodimentdepicted in FIG. 2. The processing techniques described earlier in thedescription for FIG. 2 and FIG. 3 are valid for the embodiment of FIG. 4and hence are not included herein for the brevity of the description.However, in an embodiment, the Tgap 484 defined as a time differencebetween generation of the first ramp segment 480 and the second rampsegment 482 is a negative value, since the second ramp segment 482starts prior to the ending of the first ramp segment 480 (i.e. thesecond ramp segment 482 attains its first frequency prior to the firstramp segment 480 attaining its second frequency). The embodiment of FIG.4 allows both the ramp segments (the first ramp segment 480 and thesecond ramp segment 482) to be transmitted simultaneously, thusachieving the same resolution as the embodiment of FIG. 2 but in lessertime.

FIG. 5 illustrates waveforms generated by a local oscillator 106 as afunction of time, in a radar apparatus, according to an embodiment. Thewaveforms illustrated in FIG. 5 are illustrated in connection with radarapparatus 100. The local oscillator 106 generates a plurality of rampsegments. The plurality of ramp segments includes a first ramp segment502 and a second ramp segment 504. A slope of the first ramp segment 502is equal to a slope of the second ramp segment 504.

In one example, the slope of the first ramp segment 502 is not equal tothe slope of the second ramp segment 504. In an example, the localoscillator 106 includes a PLL (phase locked loop) that generates thefirst ramp segment 502 and the second ramp segment 504. The first rampsegment 502 has a start frequency fc0 508, a first frequency fc1 510 anda second frequency fc2 512. The second ramp segment 504 has a startfrequency fc3 514, a first frequency fc4 516 and a second frequency fc5518.

In one example, the local oscillator 106 includes a first voltagecontrolled oscillator (VCO) and a second VCO that generates the firstramp segment 502 and the second ramp segment 504 respectively. Inanother example, the local oscillator 106 includes a plurality of VCO'sthat generates a plurality of ramp segments. In yet another example, thelocal oscillator 106 includes a voltage controlled oscillator (VCO). TheVCO includes a first tuning element and a second tuning element thatgenerates the first ramp segment 502 and the second ramp segment 504respectively.

In an example, a round trip delay is defined as a time differencebetween start of transmission of a ramp segment and receiving thecorresponding start of received signal from an obstacle of the one ormore obstacles. A maximum round trip delay is defined as a timedifference between start of transmission of the first ramp segment 502and start of reception of the first received signal from a farthestobstacle of the one or more obstacles. The farthest obstacle is anextreme obstacle which can be detected by the radar apparatus 100.

The start frequency is less than the first frequency by at least aproduct of an absolute value of the slope of the first ramp segment 502and the maximum round trip delay when the slope of the first rampsegment 502 and the second ramp segment 504 are equal and positive. Thestart frequency is greater than the first frequency by at least aproduct of an absolute value of the slope of the first ramp segment 502and the maximum round trip delay when the slope of the first rampsegment 502 and the second ramp segment 504 are equal and negative.

The time Tc1 520 defines a duration of the first ramp segment 502 andthe time Tc2 522 defines a duration of the second ramp segment 504. Inan embodiment, Tc1 520 is equal to Tc2 522. The time Tgap 524 includes atime taken in the local oscillator 106 to switch from the first VCO tothe second VCO or to switch from the first tuning element to the secondtuning element. In an example, the time Tgap 524 includes a timerequired for the local oscillator 106 to settle after switching from thefirst VCO to the second VCO or from the first tuning element to thesecond tuning element. The time Tgap 524 also represents a timedifference between generation of the first ramp segment 502 and thesecond ramp segment 504.

A time difference between start of transmission of the second rampsegment 504 and start of reception of the second received signal fromthe farthest obstacle of the one or more obstacles is represented as τ2540 and equals the difference of t3 and t3′. From the time instant t3534, the second VCO is assumed to be generating a steady second rampsegment 504. Similarly, τ1 538 is a time difference between start oftransmission of the first ramp segment 502 and start of reception of thefirst received signal from the farthest obstacle of the one or moreobstacles.

A difference between the second frequency fc2 512 of the first rampsegment 502 and the first frequency fc4 516 of the second ramp segment504 is equal to a product of a slope (S) of the first ramp segment 502and a time difference between the time instant when the first rampsegment 502 is at the second frequency and the time instant when thesecond ramp segment 504 is at the first frequency.

f _(c4) =f _(c2) +S(T _(gap))  (16)

The ADC 112 samples the first IF signal from a time instant t1 530 to atime instant t2 532 and generates a first valid data. The ADC 112samples the second IF signal from a time instant t3 534 to a timeinstant t4 536 to generate a second valid data. The synchronizationblock 114 provides a data valid signal to the ADC 112 during thesampling of the first IF signal and during the sampling of the second IFsignal. Thus, the synchronization block 114 synchronizes the operationof the local oscillator 106 and the ADC 112. The first valid data andthe second valid data from the ADC are provided to the DSP 116 forfurther processing.

As the difference between the second frequency fc2 512 of the first rampsegment 502 and the first frequency fc4 516 of the second ramp segment504 is equal to a product of a slope (S) of the first ramp segment 502and a time difference between generation of the first ramp segment 502and the second ramp segment 504, the DSP 116 concatenates the firstvalid data, a plurality of padding samples and the second valid data togenerate a concatenated data.

A number of padding samples in the plurality of padding samples is equalto a product of a sampling rate of the ADC 112 and the time differencebetween the time instant when the first ramp segment 502 is at thesecond frequency and the time instant when the second ramp segment 504is at the first frequency. In one example, a value of each paddingsample in the plurality of padding samples is zero. In another example,the number of padding samples in the plurality of padding samples is afunction of a product of a sampling rate of the ADC 112 and the timedifference between the time instant when the first ramp segment 502 isat the second frequency and the time instant when the second rampsegment 504 is at the first frequency.

The DSP 116 further performs fast fourier transform on the concatenateddata to generate an FFT vector such that the FFT vector is processed toestimate a range of the obstacle of the one or more obstacles. In oneversion, a plurality of first valid data and a plurality of second validdata is obtained when a plurality of the first ramp segments and aplurality of the second ramp segments are transmitted by the radarapparatus i.e. the transmission being in an interleaved manner withevery transmission of the first ramp segment 502 being followed by atransmission of the second ramp segment 504 (as illustrated in FIG. 5).A 2D FFT (2 dimensional fast fourier transform) is performed on theobtained valid data to estimate velocity of the one or more obstacles.

The DSP 116 is oblivious to the fact that the concatenated data wasgenerated using multiple VCO's that generates multiple ramps segmentswith a time difference between consecutive ramp segments. The DSP 116processes the concatenated data as if the transmit signal was a singleramp from frequency fc1 510 to frequency fc5 518. It is understood thatthe above procedure is explained using an embodiment with the first rampsegment 502 and the second ramp segment 504 and it can be extended to aplurality of ramp segments by repeating the same procedure.

Thus, the bandwidth of a transmitted signal from the radar apparatus 100is increased by transmitting a plurality of ramp segments and therebyimproving the range resolution of the radar apparatus 100 without beinglimited by the range of a single VCO or of a tuning element. Further theembodiments used to generate the concatenated data are transparent to asignal processing software that resides on the DSP 116 and performs theradar signal processing.

Importantly the FFT processing (including 2D FFT processing) on the DSP116 will be independent of the time Tgap 524 between the ramp segmentsand will operate as if a single ramp from fc1 510 to fc5 518 weretransmitted by the local oscillator 106. Hence, the signal processingsoftware residing on the DSP 116 will require little or no customizationin order to process ADC samples obtained using the above describedembodiments. However, it should be noted that depending on the length ofthe time Tgap 524 between the ramp segments, there can be side-lobesintroduced in the spectrum after FFT processing. Thus, the detectionprocesses that follow the FFT processing must be cognizant of this fact.

In the foregoing discussion, the terms “connected” means at least eithera direct electrical connection between the devices connected or anindirect connection through one or more passive intermediary devices.The term “circuit” means at least either a single component or amultiplicity of passive or active components, that are connectedtogether to provide a desired function. The term “signal” means at leastone current, voltage, charge, data, or other signal. Also, the terms“connected to” or “connected with” (and the like) are intended todescribe either an indirect or direct electrical connection. Thus, if afirst device is coupled to a second device, that connection can bethrough a direct electrical connection, or through an indirectelectrical connection via other devices and connections.

It should be noted that reference throughout this specification tofeatures, advantages, or similar language does not imply that all of thefeatures and advantages should be or are in any single embodiment.Rather, language referring to the features and advantages is understoodto mean that a specific feature, advantage, or characteristic describedin connection with an embodiment is included in at least one embodimentof the present disclosure. Thus, discussion of the features andadvantages, and similar language, throughout this specification may, butdo not necessarily, refer to the same embodiment.

Further, the described features, advantages, and characteristics of thedisclosure may be combined in any suitable manner in one or moreembodiments. One skilled in the relevant art will recognize that thedisclosure can be practiced without one or more of the specific featuresor advantages of a particular embodiment. In other instances, additionalfeatures and advantages may be recognized in certain embodiments thatmay not be present in all embodiments of the disclosure.

One having ordinary skill in the art will understand that the presentdisclosure, as discussed above, may be practiced with steps and/oroperations in a different order, and/or with hardware elements inconfigurations which are different than those which are disclosed.Therefore, although the disclosure has been described based upon thesepreferred embodiments, it should be appreciated that certainmodifications, variations, and alternative constructions are apparentand well within the spirit and scope of the disclosure. In order todetermine the metes and bounds of the disclosure, therefore, referenceshould be made to the appended claims.

What is claimed is:
 1. A radar apparatus comprising: a local oscillatorconfigured to generate a first ramp segment and a second ramp segment, aslope of the first ramp segment and a slope of the second ramp segmentare equal and positive, and wherein the first ramp segment and thesecond ramp segment each comprising a start frequency, a first frequencyand a second frequency, and wherein the first frequency of the secondramp segment is equal to or greater than the second frequency of thefirst ramp segment; and a transmit antenna unit coupled to the localoscillator and configured to transmit the first ramp segment and thesecond ramp segment.
 2. The radar apparatus of claim 1, furthercomprising: a receive antenna unit configured to receive a firstreceived signal and a second received signal, wherein the first receivedsignal and the second received signal are generated from the first rampsegment and the second ramp segment respectively; a receiver front-endcoupled to the receive antenna unit and configured to amplify the firstreceived signal and the second received signal; a mixer coupled to thereceiver front-end and configured to mix the first ramp segment and thefirst received signal to generate a first IF (intermediate frequency)signal and configured to mix the second ramp segment and the secondreceived signal to generate a second IF signal; an analog to digitalconverter (ADC) coupled to the mixer and configured to sample the firstIF signal to generate a first valid data and configured to sample thesecond IF signal to generate a second valid data; and a digital signalprocessor (DSP) coupled to the ADC and configured to process a dataformed from the first valid data and the second valid data.
 3. The radarapparatus of claim 2, wherein the ADC is configured to sample the firstIF signal only from a time instant when the first ramp segment is at thefirst frequency to a time instant when the first ramp segment is at thesecond frequency and configured to sample the second IF signal only froma time instant when the second ramp segment is at the first frequency toa time instant when the second ramp segment is at the second frequency.4. The radar apparatus of claim 1, wherein the start frequency of thefirst ramp segment is less than the first frequency of the first rampsegment by at least a product of the slope of the first ramp segment anda maximum round trip delay and, wherein a time difference between startof transmission of the first ramp segment and start of reception of thefirst received signal from a farthest obstacle of the one or moreobstacles is the maximum round trip delay.
 5. The radar apparatus ofclaim 1, wherein the local oscillator further comprises a plurality ofvoltage controlled oscillators (VCO's) configured to generate aplurality of ramp segments, the plurality of ramp segments includes thefirst ramp segment and the second ramp segment, and wherein a timedifference between the time instant when the first ramp segment is atthe second frequency and a time instant when the second ramp segment isat the start frequency is equal to a time difference between generationof the first ramp segment and the second ramp segment by the localoscillator.
 6. The radar apparatus of claim 1, wherein a start of thesecond ramp segment is before an end of the first ramp segment.
 7. Theradar apparatus of claim 1 further comprising a synchronization blockcoupled to the local oscillator and to the ADC, the synchronizationblock configured to provide a data valid signal to the ADC duringsampling of the first IF signal and during sampling of the second IFsignal.
 8. The radar apparatus of claim 1, wherein the DSP is configuredto process the data formed from the first valid data and the secondvalid data using at least one of a concatenation technique, a modifiedconcatenation technique, a modified 1D-FFT technique and a modified2D-FFT technique, when the second frequency of the first ramp segment isequal to the first frequency of the second ramp segment.
 9. The radarapparatus of claim 8, wherein the DSP is configured to compare athreshold and a product of a velocity estimate of an obstacle of the oneor more obstacles and the time difference between the time instant whenthe first ramp segment is at the second frequency and the time instantwhen the second ramp segment is at the start frequency.
 10. The radarapparatus of claim 9, wherein: when the product of the velocity estimateof the obstacle and the time difference between the time instant whenthe first ramp segment is at the second frequency and the time instantwhen the second ramp segment is at the start frequency is below thethreshold, the DSP is configured to perform the concatenation technique;and when the product of the velocity estimate of the obstacle and thetime difference between the time instant when the first ramp segment isat the second frequency and the time instant when the second rampsegment is at the start frequency is above the threshold, the DSP isconfigured to perform at least one of the modified concatenationtechnique, the modified 1D-FFT technique and the modified 2D-FFTtechnique.
 11. The radar apparatus of claim 10, wherein in theconcatenation technique, the DSP is configured to: concatenate the firstvalid data and the second valid data to generate a concatenated data;and perform fast fourier transform (FFT) on the concatenated data togenerate an FFT vector such that the FFT vector is processed to estimatea range of an obstacle.
 12. The radar apparatus of claim 10, wherein inthe modified concatenation technique, the DSP is configured to: multiplythe second valid data with a complex phasor to generate a modifiedsecond valid data; concatenate the first valid data and the modifiedsecond valid data to generate a concatenated data; and perform fastfourier transform on the concatenated data to generate an FFT vectorsuch that the FFT vector is processed to estimate a range of anobstacle.
 13. The radar apparatus of claim 10, wherein in the modified1D-FFT (1-dimensional fast fourier transform) technique, the DSP isconfigured to: perform fast fourier transform on the first valid dataand the second valid data to generate a first FFT vector and a secondFFT vector respectively, the first FFT vector and the second FFT vectoreach comprising a plurality of elements; multiply each element of theplurality of elements of the second FFT vector with a complex phasor togenerate a modified second FFT vector, wherein a phase of the complexphasor is a function of an index of an element of the second FFT vectorand the product of the velocity estimate of the obstacle and the timedifference between the time instant when the first ramp segment is atthe second frequency and the time instant when the second ramp segmentis at the start frequency; and add the modified second FFT vector andthe first FFT vector to generate a single FFT vector such that thesingle FFT vector is processed to estimate the range of the obstacle.14. The radar apparatus of claim 10, wherein in the modified 2D-FFT(2-dimensional fast fourier transform) technique, the DSP is configuredto: perform a zero padded 2D-FFT (2-dimensional fast fourier transform)on a plurality of the first valid data and on a plurality of the secondvalid data to generate a first 2D FFT array and a second 2D FFT arrayrespectively, the first 2D FFT array and the second 2D FFT array eachcomprising a plurality of elements arranged in a 2D matrix indexed bytwo indices and, wherein the plurality of the first valid data isobtained from a plurality of the first ramp segments and the pluralityof the second valid data is obtained from a plurality of the second rampsegments; multiply each element of the plurality of elements of thesecond 2D FFT array with a complex phasor to generate a modified second2D FFT array, wherein a phase of the complex phasor is a function of thetwo indices and the time difference between the time instant when thefirst ramp segment is at the second frequency and the time instant whenthe second ramp segment is at the start frequency; and add the modifiedsecond 2D FFT array and the first 2D FFT array to generate a single 2DFFT array such that the single 2D FFT array is processed to estimate arange and velocity of the one or more obstacles.
 15. The radar apparatusof claim 10, wherein to obtain the velocity estimate of the obstacle:the local oscillator is configured to generate a plurality of the firstramp segments; the transmit antenna unit is configured to transmit theplurality of first ramp segments; the receive antenna unit is configuredto receive a plurality of first received signals, wherein a plurality ofthe first received signals are generated from the plurality of the firstramp segments; the mixer is configured to mix the plurality of firstramp segments and the plurality of the first received signals to generate a plurality of IF signals; the ADC is configured to sample theplurality of IF signals; and the DSP is configured to perform fastfourier transform (FFT) on the plurality of IF signals.
 16. The radarapparatus of claim 1, wherein the second frequency of the first rampsegment is not equal to the first frequency of the second ramp segment,and the DSP is configured to: concatenate the first valid data, aplurality of padding samples and the second valid data to generate aconcatenated data; and perform fast fourier transform on theconcatenated data to generate an FFT vector such that the FFT vector isprocessed to estimate a range of an obstacle.
 17. The radar apparatus ofclaim 1, wherein a difference between the second frequency of the firstramp segment and the first frequency of the second ramp segment is equalto a product of the slope of the first ramp segment and the timedifference between the time instant when the first ramp segment is atthe second frequency and the time instant when the second ramp segmentis at the first frequency, and the DSP is configured to: concatenate thefirst valid data, a plurality of padding samples and the second validdata to generate a concatenated data; and perform fast fourier transformon the concatenated data to generate an FFT vector such that the FFTvector is processed to estimate a range of an obstacle.
 18. The radarapparatus of claim 17, wherein a number of padding samples in theplurality of padding samples is equal to a product of a sampling rate ofthe ADC and the time difference between the time instant when the firstramp segment is at the second frequency and the time instant when thesecond ramp segment is at the first frequency.
 19. The radar apparatusof claim 17, wherein a value of each padding sample in the plurality ofpadding samples is zero.
 20. A method comprising: receiving a firstreceived signal and a second received signal; mixing a first rampsegment and the first received signal to generate a first IF(intermediate frequency) signal and mixing a second ramp segment and thesecond received signal to generate a second IF signal; sampling thefirst IF signal in an analog to digital converter (ADC) to generate afirst valid data and sampling the second IF signal to generate a secondvalid data; and processing a data formed from the first valid data andthe second valid data, wherein the first IF signal is sampled only froma time instant when the first ramp segment is at a first frequency to atime instant when the first ramp segment is at a second frequency andthe second IF signal is sampled only from a time instant when the secondramp segment is at the first frequency to a time instant when the secondramp segment is at the second frequency, and wherein the first frequencyof the second ramp segment is equal to or greater than the secondfrequency of the first ramp segment.
 21. The method of claim 20 furthercomprising: transmitting the first ramp segment and the second rampsegment, a slope of the first ramp segment and a slope of the secondramp segment are equal and positive, and wherein the first ramp segmentand the second ramp segment each comprise a start frequency, the firstfrequency and the second frequency; and generating the first receivedsignal and the second received signal from the first ramp segment andthe second ramp segment respectively.
 22. The method of claim 21,wherein the start frequency of the first ramp segment is less than thefirst frequency of the first ramp segment by at least a product of theslope of the first ramp segment and a maximum round trip delay andwherein a time difference between start of transmission of the firstramp segment and start of reception of the first received signal from afarthest obstacle of the one or more obstacles is the maximum round tripdelay.
 23. The method of claim 21 wherein the second frequency of thefirst ramp segment is equal to the first frequency of the second rampsegment and the method further comprises performing a concatenationtechnique; the concatenation technique comprising: concatenating thefirst valid data and the second valid data to generate a concatenateddata; and performing fast fourier transform (FFT) on the concatenateddata to generate an FFT vector, wherein the FFT vector is processed toestimate a range of an obstacle.
 24. The method of claim 21, wherein thesecond frequency of the first ramp segment is equal to the firstfrequency of the second ramp segment and the method further comprisesperforming a modified concatenation technique, the modifiedconcatenation technique comprising: multiplying the second valid datawith a complex phasor to generate a modified second valid data;concatenating the first valid data and the modified second valid data togenerate a concatenated data; and performing fast fourier transform onthe concatenated data to generate an FFT vector, wherein the FFT vectoris processed to estimate a range of an obstacle.
 25. The method of claim21, wherein the second frequency of the first ramp segment is equal tothe first frequency of the second ramp segment and the method furthercomprises performing a modified 1D-FFT technique, the modified 1D-FFTtechnique comprising: performing fast fourier transform on the firstvalid data and the second valid data to generate a first FFT vector anda second FFT vector respectively, the first FFT vector and the secondFFT vector each comprising a plurality of elements; multiplying eachelement of the plurality of elements of the second FFT vector with acomplex phasor to generate a modified second FFT vector, wherein a phaseof the complex phasor is a function of an index of an element of thesecond FFT vector and the product of a velocity estimate of the obstacleand a time difference between the time instant when the first rampsegment is at the second frequency and the time instant when the secondramp segment is at the first frequency; and adding the modified secondFFT vector and the first FFT vector to generate a single FFT vector,wherein the single FFT vector is processed to estimate a range of anobstacle.
 26. The method of claim 21, wherein the second frequency ofthe first ramp segment is equal to the first frequency of the secondramp segment and the method further comprises performing a modified2D-FFTtechnique, the modified 2D-FFT technique comprising: performing azero padded 2D-FFT (2-dimensional fast fourier transform) on a pluralityof the first valid data and on a plurality of the second valid data togenerate a first 2D FFT array and a second 2D FFT array respectively,the first 2D FFT array and the second 2D FFT array each comprising aplurality of elements arranged in a 2D matrix indexed by two indicesand, wherein the plurality of the first valid data is obtained from aplurality of the first ramp segments and the plurality of the secondvalid data is obtained from a plurality of the second ramp segments;multiplying each element of the plurality of elements of the second 2DFFT array with a complex phasor to generate a modified second 2D FFTarray, wherein a phase of the complex phasor is a function of the twoindices and the time difference between the time instant when the firstramp segment is at the second frequency and the time instant when thesecond ramp segment is at the first frequency; and adding the modifiedsecond 2D FFT array and the first 2D FFT array to generate a single 2DFFT array, wherein the single 2D FFT array is processed to estimate arange and velocity of one or more obstacles.
 27. The method of claim 21,wherein when the difference between the second frequency of the firstramp segment and the first frequency of the second ramp segment is equalto a product of the slope of the first ramp segment and the timedifference between the time instant when the first ramp segment is atthe second frequency and the time instant when the second ramp segmentis at the first frequency, the method further comprising: concatenatingthe first valid data, a plurality of padding samples and the secondvalid data to generate a concatenated data; and performing fast fouriertransform on the concatenated data to generate an FFT vector such thatthe FFT vector is processed to estimate a range of an obstacle.
 28. Themethod of claim 27, wherein a number of padding samples in the pluralityof padding samples is equal to a product of a sampling rate of the ADCand the time difference between the time instant when the first rampsegment is at the second frequency and the time instant when the secondramp segment is at the first frequency and, wherein a value of eachsample in the plurality of padding samples is zero.